Meteorites and their components have anomalous oxygen isotopic compositions characterized by large variations in 18O/16O and 17O/16O ratios. On the basis of recent observations of star-forming regions and models of accreting protoplanetary disks, we suggest that these variations may originate in a parent molecular cloud by ultraviolet photodissociation processes. Materials with anomalous isotopic compositions were then transported into the solar nebula by icy dust grains during the collapse of the cloud. The icy dust grains drifted toward the Sun in the disk, and their subsequent evaporation resulted in the 17O- and 18O-enrichment of the inner disk gas.